The Generalized Voronoi Graph (GVG) has been effectively used for the SLAM and navigation of mobile robots. Since the mobile robot should perform the GVG-based SLAM and navigation in unstructured environments using inaccurate noisy sensors, it requires accurate data association and robust navigation techniques. in this paper, we suggest three techniques for a robust construction of the GVG. The first one is a robust node matching technique and the second one is an adaptable sensor area matching method for the robust exploration. Finally we propose a technique which is capable of distinguishing between closely located nodes. The simulation results show that the proposed algorithm can work successfully under 20% errors of odometry and range sensor in unstructured environment.